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<Title>Confidence Band</Title>
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<p class="heading0">ChartDirector 7.0 (Java Edition)</p>
<p class="heading1">Confidence Band</p>
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<img src="images/confidenceband.png" width='450' height='420'>
<br><br>
This example demonstrates adding confidence bands to a trend line. It also demonstrates how to display linear regression parameters on the chart.<br><br>
In linear regression, the data points are assumed to be related by:<br><br>
<div class="indentedblock"><code>y = m * x + c + err</code></div><br>
where m and c are constants, and err is a random variable. Linear regression estimates m, c and err based on available data.<br><br>
As m and c are estimated values, the trend line y = m * x + c may be inaccurate. In ChartDirector, the uncertainties can be represented as a confidence band using <a href="TrendLayer.addConfidenceBand.htm">TrendLayer.addConfidenceBand</a>. For example, the 95% confidence band means there are 95% probability that the "real" trend line is in that band.<br><br>
To predict a data point (infer y given x), we use y = m * x + c + err. As m, c and err are estimated values, the predicted data point may be inaccurate. In ChartDirector, the uncertainties can be represented as a prediction band using <a href="TrendLayer.addPredictionBand.htm">TrendLayer.addPredictionBand</a>.<br><br>
Note that the prediction band is always wider than the confidence band because of the extra uncertainties contributed by the err term.<br><br>
In ChartDirector, the linear regression parameters slope, intercept, correlation coefficient and standard error can be obtained by using <a href="TrendLayer.getSlope.htm">TrendLayer.getSlope</a>, <a href="TrendLayer.getIntercept.htm">TrendLayer.getIntercept</a>, <a href="TrendLayer.getCorrelation.htm">TrendLayer.getCorrelation</a> and <a href="TrendLayer.getStdError.htm">TrendLayer.getStdError</a>. (Please refer to appropriate statistics text books for explanation of these values.)<br><br>
In this example, the linear regression parameters are formatted into a table using <a href="cdml.htm">CDML</a>, which is then added to the chart as custom text box using <a href="BaseChart.addText.htm">BaseChart.addText</a>.
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<p class="heading1a">Source Code Listing</p>
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<b>[JSP Version]</b> jspdemo/confidenceband.jsp
<div class='codeblock'><code class='pre'>&lt;%@page import="ChartDirector.*, java.util.*" %&gt;
&lt;%
// The XY data of the first data series
double[] dataX = {50, 55, 37, 24, 42, 49, 63, 72, 83, 59};
double[] dataY = {3.6, 2.8, 2.5, 2.3, 3.8, 3.0, 3.8, 5.0, 6.0, 3.3};

// Create a XYChart object of size 450 x 420 pixels
XYChart c = new XYChart(450, 420);

// Set the plotarea at (55, 65) and of size 350 x 300 pixels, with white background and a light grey
// border (0xc0c0c0). Turn on both horizontal and vertical grid lines with light grey color
// (0xc0c0c0)
c.setPlotArea(55, 65, 350, 300, 0xffffff, -1, 0xc0c0c0, 0xc0c0c0, -1);

// Add a title to the chart using 18 point Times Bold Itatic font.
c.addTitle("Server Performance", "Times New Roman Bold Italic", 18);

// Add titles to the axes using 12pt Arial Bold Italic font
c.yAxis().setTitle("Response Time (sec)", "Arial Bold Italic", 12);
c.xAxis().setTitle("Server Load (TPS)", "Arial Bold Italic", 12);

// Set the axes line width to 3 pixels
c.yAxis().setWidth(3);
c.xAxis().setWidth(3);

// Add a scatter layer using (dataX, dataY)
ScatterLayer scatterLayer = c.addScatterLayer(dataX, dataY, "", Chart.DiamondSymbol, 11, 0x008000);

// tool tip for scatter layer
scatterLayer.setHTMLImageMap("", "", "title='Response time at {x} TPS: {value} sec'");

// Add a trend line layer for (dataX, dataY)
TrendLayer trendLayer = c.addTrendLayer2(dataX, dataY, 0x008000);

// Set the line width to 3 pixels
trendLayer.setLineWidth(3);

// Add a 95% confidence band for the line
trendLayer.addConfidenceBand(0.95, 0x806666ff);

// Add a 95% confidence band (prediction band) for the points
trendLayer.addPredictionBand(0.95, 0x8066ff66);

// tool tip for trend layer
trendLayer.setHTMLImageMap("", "",
    "title='Slope = {slope|4} sec/TPS; Intercept = {intercept|4} sec'");

// Add a legend box at (50, 30) (top of the chart) with horizontal layout. Use 10pt Arial Bold
// Italic font. Set the background and border color to Transparent.
LegendBox legendBox = c.addLegend(50, 30, false, "Arial Bold Italic", 10);
legendBox.setBackground(Chart.Transparent);

// Add entries to the legend box
legendBox.addKey("95% Line Confidence", 0x806666ff);
legendBox.addKey("95% Point Confidence", 0x8066ff66);

// Display the trend line parameters as a text table formatted using CDML
TextBox textbox = c.addText(56, 65, String.format(
    "&lt;*block*&gt;Slope\nIntercept\nCorrelation\nStd Error&lt;*/*&gt;   &lt;*block*&gt;%.4f sec/tps\n%.4f sec\n" +
    "%.4f\n%.4f sec&lt;*/*&gt;", trendLayer.getSlope(), trendLayer.getIntercept(),
    trendLayer.getCorrelation(), trendLayer.getStdError()), "Arial Bold", 8);

// Set the background of the text box to light grey, with a black border, and 1 pixel 3D border
textbox.setBackground(0xc0c0c0, 0, 1);

// Output the chart
WebChartViewer viewer = new WebChartViewer(request, "chart1");
viewer.setChart(c, Chart.SVG);

// include tool tip for the chart
viewer.setImageMap(c.getHTMLImageMap(""));
%&gt;
&lt;!DOCTYPE html&gt;
&lt;html&gt;
&lt;head&gt;
    &lt;title&gt;Confidence Band&lt;/title&gt;
    &lt;!-- Include ChartDirector Javascript Library to support chart interactions --&gt;
    &lt;script type="text/javascript" src="cdjcv.js"&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body style="margin:5px 0px 0px 5px"&gt;
    &lt;div style="font:bold 18pt verdana;"&gt;
        Confidence Band
    &lt;/div&gt;
    &lt;hr style="border:solid 1px #000080; background:#000080" /&gt;
    &lt;div style="font:10pt verdana; margin-bottom:1.5em"&gt;
        &lt;a href="viewsource.jsp?file=&lt;%=request.getServletPath()%&gt;"&gt;View Source Code&lt;/a&gt;
    &lt;/div&gt;
    &lt;!-- ****** Here is the chart image ****** --&gt;
    &lt;%= viewer.renderHTML(response) %&gt;
&lt;/body&gt;
&lt;/html&gt;</code></div>
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